A New Action Principle for Witten's Topological Field Theory

TL;DR

This paper introduces a new gauge-invariant, metric-independent action for Witten's topological field theory, with an off-shell BRST algebra, offering a geometric foundation for the quantum theory and comparing it to existing formulations.

Contribution

It presents a novel action principle with off-shell BRST closure, enhancing the geometric understanding of Witten's topological quantum field theory.

Findings

New gauge-invariant, metric-independent action introduced

BRST algebra closes off-shell in the new formulation

Comparison with existing models shows advantages in geometric interpretation

Abstract

In this letter a new gauge invariant, metric independent action is introduced from which Witten's Topological Quantum Field Theory may be obtained after gauge fixing using standard BRST techniques. In our model the BRST algebra of transformations, under which the effective action is invariant, close off-shell in distintion with what occurs in the one proposed by Labastida and Pernici. Our approach provides the geometrical principle for the quantum theory. We also compare our results with an alternative formulation presented by Baulieu and Singer.